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S. L. Robinson, B.%. Odegard, Jr., N. R. Mood~, S.-H. Goods

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SAND2000-8243Unlimited ReleasePrinted June 2000

An Analysis ofBurst Disc Pressure Instability

Steven L. RobinsonGTS and Microengineering Department

Ben C. Odegard, Jr.Engineered Materials Department

Neville R. Moody and Steven H. GoodsMaterials Mechanics DepartmentSandia National Laboratories/CA

AbstractDuring the development stage of the 1X Acorn burst disc, burst pressure test resultsexhibited an unexpected increase of 8 to 14910over times of 90-100 days from initialfabrication. This increase is a concern where design constraints require stability. Thedisc material, 316L stainless steel sheet, is formed to a dome-like geometry and scored toproduce a thin-walled, high-strength ligament. The fracture events controlling burstoccur in that ligament. Thus it has been characterized both for tensile properties andmicrostructure through nanoindentation, magnetic measurements, optical andtransmission electron microscopy. These results compare favorably with finite elementsimulation of the properties of the ligament.

The ligament exhibits a highly heterogeneous microstructure; it’s small volume andmicrostructural heterogeneity make it difficult to identify which microstructural featurecontrols fracture and hence burst pressure. Bulk mechanical test specimens werefabricated to emulate mid-ligament properties, and aged at both room and elevatedtemperatures to characterize and accelerate the temporal behavior of the burst disc.Property changes included yield and ultimate tensile strength increases, and fracturestrain decreases with aging. Specimens were subjected to a reversion anneal identical tothat given the burst disc to eliminate the martensite phase formed during rolling.Reversion-annealed samples exhibited no change in properties in room temperature oraccelerated aging, showing that the reversion-anneal eliminated the aging phenomenon.Aging was analyzed in terms of diffusion controlled precipitate growth kinetics, showingthat carbon migration to dislocations is consistent with the strength increases. A

3

vacancy-assisted diffusion mechanism for carbon transport is proposed, giving rise torapid aging, which replaces interstitial carbon diffusion until excess vacancies fromdeformation are consumed. Mechanical activation parameters in stress relaxation weremeasured, indicating that the deformation structures formed at high strains typical of thescore ligament are resistant to annealing, and rnimick the behavior of athermal obstacles.This model also qualitatively explains the different rates of aging resulting from a rangeof levels of cold work.

‘

TABLE OF CONTENTS

Introduction

Characterization of Burst Disc Microstructure

Experimental ProceduresMechanical Testing and Accelerated Aging

ResultsMechanical Testing and Thermal Aging

DiscussionAnalysis of the Activation EnergyAnalysis of the Kinetics of the Rate of Strength IncreaseLimitations of the Study

Conclusions

Acknowledgements

AppendicesA. Hypothesis for the Mechanism Controlling

Time Dependent StrengtheningB. Analysis of the Activation Energy Utilizing

Vacancy-assisted Accelerated DiffusionC. Quantification of Thermal Acceleration of AgingD. Kinetics of Aging in Different MicrostructureE. Activation Volume

m

.

5

7

10

1213

1314

20202122

23

24

25

25

25262627

ILLUSTRATIONS

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

Figure 9.

Figure 10.

Figure 11.

Figure 12.

Burst disc assembly, metallographic cross section of burst disc score,and schematic of fracture cross-section.

Computed strain contours from Chiesa7 for the as-formed burstdisc score.

Nanoindentation results for flow stress beneath the score mark in aburst disc annealed at 704°C (1300°F) / 0.75 hour..

Tensile behavior of rolled stainless steel specimens.

Effect of 250”C thermal age on the stress-strain curves for 75%cold-rolled stainless steel.

Evolution in strength with aging time at 250”C.

Strain to onset of plastic instability increases with increasingaging time.

Influence of aging temperature on mechanical properties of 75%cold-worked stainless steel.

Tensile properties of reversion annealed cold worked stainless steel.

Tensile properties of reversion annealed stainless steel are unaffectedby thermal aging.

A sample stress relaxation curve for 75% cold rolled stainless steel.

A Reciprocal activation volume normalized to b3 as a function offlow stress for as-rolled and reversion annealed 3 16L stainless steel.B. Activation volumes for other alloys are shown for comparison[from Moody et al”] at small values of b3/V.

Tables

8

10

11

15

15

17

17

18

18

19

19

21

6

Table I. Composition of the 3 16L bar stock in wt. % 13

Table II. Accelerated aging studies test matrix 13

Table III. Tensile properties of replicate as-rolled specimen cold rolled to 75thickness reduction 96 14

An Analysis ofBurst Disc Pressure Instability

Introduction

The burst disc under consideration, shown in Figure 1, is a subassembly of the 1-XAcorn. Earlydevelopment parts exhibited aburstpressure instability inwhich the burstpressure rose quickly in the first weeks following forming, and asymptoticallyapproached a burst pressure some 8-14% higher than that measured immediate y afterforming. The presence ofmartensiteinthe316L stainless steel disc was also identified inthe region of the score ligament, by magnetic and by metallographic means. Thepresence of martensite in 3 16L is considered unusual since 3 16L is usually resistant todeformation-induced phase changes. A 732°C partial anneal was developed to revert themartensite to austenite, in order to improve hydrogen compatibility. As-formed discswere then subjected to this reversion-anneal immediately following forming.Subsequently, it was observed that the time-dependent burst pressure increase (referred toas aging) ceased, based on a six month observation. A long-term issue to be addressed isthen whether the aging phenomenon has been conclusively stopped by the reversionanneal. Identification and description of the mechanism(s) responsible for the agingphenomenon is crucial to gaining confidence in the long-term stability of the burstpressure.

In a previous studyl it was observed that the burst disc ligament immediately below thescore mark controlled fracture, and hence the burst pressure, of the disc. When the disc isfunctioned, stable ductile rupture begins at the back or unscored surface*, transitioning toan unstable shear fracture at a depth of roughly 10-15 pm. The shear fracture thenrapidly propagates inward from the ductile fracture initiation site to the root of the scoreregion. Simultaneously, the fracture moves rapidly outward along two fronts followingthe score, and terminating at the ends of the score.

The strength of the ligament must increase for an increase in burst pressure to occur.Experimentally we observe that, as the burst pressure increases, the dome (marked “disk”in Figure 1) grows plastically to a greater extent prior to the fracture event. The domegrowth introduces work hardening in the dome, which, once strong enough, transfers loadand deformation to the score ligament. This process implies a higher strength in theIigamentl.

The source of the strength increase with time is not immediately obvious, in that stainlesssteels such as low interstitial 3 16L stainless steel are not commonly considered to exhibiteither thermal or strain aging at room temperature. We note, though, that the degree ofdeformation within the score ligament is quite intense and therefore, the aging response

1Memo,S.L.Robinsonto Distribution,October1, 1998,“Analysisof BurstDiscFailureModes”

7

—----- . . ... .- . ..... -,--- ---.Y---- ,...., - -> s--,-- - . . .. 7.. ---- , . . . . . . .,:. :- -- , ?.7-

Inner surface of disc

Outer surface of disc

Inner surface of burst disc

Scored sutiacesApproximate 45 degree shear

Ductile rupture zone

Shear fracture zone

Initiation zone (ductile rupture*)

*Except in the hydrogen embrittled case

angle

Figure 1. Burst disc assembly, metallographic cross section of burst disc score, and schematic offracture cross-section.

of the alloy may be atypical. Data from Meye# indicate the presence of a time-dependentburst pressure increase suggestive of strain-aging. Strain aging of austenite is nowestablished as a known phenomenon3”b, although typically it is not observed intechnological alloys, with the exception of 316 and AISI 330’. Rose and Glover3examined iron-nickel-carbon alloys, and observed yield point phenomena in which themagnitude of the yield point, observed upon reloading from stress relaxation, wasdependent upon prior strain. Carbon was found essential to the process. Jenkins andSmith’ observed serrated flow, evidence of a Portevin-LeChatelier effect in Fe/35Ni, andin type 330 stainless steel. In the temperature range 200-500’C, carbon was believedresponsible for the interactions between solute atoms and dislocations. Hannula,Korhonen and Li5 observed yield point phenomena following prestraining and stressrelaxation at room temperature in type 316 stainless steel. They attribute the effect tocarbon-vacancy complexes interacting with dislocations, as did the previous authors,assuming that higher mobility would result from such a complex than for carbon alone.Their carbon concentration was 0.07w/o whereas the 3 16L under consideration has lessthan 0.03w/o carbon, raising the question of relevance to the behavior of 3 16L.Nevertheless, an extrapolation of their yield point results to conditions of prestrain andhold times typical of the burst disc predicts a strength increment simikir to the lowerbound of the observed burst pressure increase, that is, about an 8% increment. Thissimilarity has lent support to the idea that the disc is experiencing strain aging. Ulitchneyand Gibalab explored internal friction and serrated flow behavior over the interval of 25°Cto 400”C, in Fe/30Ni, Fe/36Ni, Invar, and 310 stainless steel. They correlated thepresence of bound peak pair-caused (BPP) internal friction peaks (C-vacancy pairs) withjerky or serrated flow in plastic deformation, and demonstrated that not only is carbonessential to the process, but excess vacancy introduction enhances the BPP internalfriction peak. The internal friction peak maximizes at about 250”C. From their results itmay be inferred that at carbon concentrations typical of 3 16L, only extremely heavilyworked structures of high dislocation density and thus high vacancy concentrationsintroduced by the deformation should exhibit BPP-derived internal friction, serrated flow,or strain aging. The necessary high strain deformation conditions may exist in therupture disc score region. Thus, by introducing an extreme deformation state in thefracture zone of the disc (the score ligament), we may have introduced both strain-induced martensite and strain aging in a material that does not commonly exhibit either.

The fracture controlling zone of the burst disc is that region beginning approximately 10~m (about 20% of the ligament thickness) below the outside or unscored surface of thedisc and opposite the apex of the score. This region is very heterogeneous, exhibitinglarge gradients in cold work, in hardness and therefore in tensile properties. In addition,within this region the fracture transitions from a stable, ductile fracture mechanism to a

2B. Meyer,LANL,unpublisheddata, 1998.3K.S.B.Rose,S.G.Glover,“AStudyof Strain-Agingin Austenite”,Acts Metall.U, p. 1505,1966.4C.F.Jenkinsand G.V.Smith,“SerratedPlasticFlowin AusteniticStainlessSteels”,Trans.Met.Sot. OfAIME,w, p. 2149, 1969.5S.P. Hannula,M.A.Korhonen,C.Y.Li, “StrainAgingand LoadRelaxationBehaviorofType316StainlessSteelat RoomTemperature,Metall.Trans.A,~, p. 1757,1986.bM.G.Ulitchney,R. Gibala,“InternalFrictionandStrainAgingof FerrousAustenite”,Metall.Trans.4,p.497,1973.

9

high velocity shear fracture. In order to examine aging behaviors and their relationship tomicrostructure, it is desirable to emulate the appropriate (fracture-controlling) ligamentmicrostructure in macroscopic specimens, which are more amenable to conventionalexamination. First, it is necessary to characterize the fracture zone. In the following, wedescribe the results of efforts to characterize the strength, microstructure and propertiesof the burst disc. These efforts will allow us to design an emulation technique forproducing useful specimen geometries with appropriate properties. The specimens maythen be examined for their aging response in real-time and accelerated aging modes.

Characterization of Burst Disc Microstructure

Finite element simulation of the formation of burst discs shows true strain levels up to 2.2in the scored region7. Figure 2 shows these strain contours as computed by Chiesa7. Theassociated flow stress at a true strain of 1.4 (the midline of the ligament) is of the order of1300 MPa (190 ksi). Magnetic examination of the back surface of the score region wasconducted using a Foerster@ “ferritegage”. Readings of 0.2-0.3% were obtained(readings away from the score were zero); these values are uncalibrated since the sensorinterrogates a 3 mm diameter volume in front of the tip; calibration requires a minimumthickness of 3 mm. We may approximate a correction factor based upon volumeconsiderations. Using the affected volume of the foil divided by the interrogated volumeof the instrument, we arrive at an approximate ratio of 1/30. Therefore a reading ofapproximately 0.20 to 0.33% would equate to 6 to 10% magnetic phase in the smallvolume. This is consistent with metallographic observations, although localconcentrations might exceed 10% martensite.

a= B.28E+BEt

b- t3.55E+0El

C“ 13.83 E+EIEI

d= EI. llE+t31

e= B. 14E+BI

f- EI.16E+!31

9“ E.19Ei-t31

h= EI.22E+BI

Midline / ID

Figure 2. Computed strain contours from Chiesa7 for the as-formed burst disc score. Themidline is midway between the score root and the back surface.

7M. Chiesa,Org.8727,SandiaNationalLaboratories,to be published.

10

The strength and hardness distribution within the score region were characterized usingnanoindentation. An example is shown below in Figure 3 for an intermediate anneal of704°C (1300”F) / 0.75 Hr. The example is that of the annealed disc, in which flowstresses have been fully corrected for indentation size effects. Midline flow stresses of upto 1.4 GPa (203 ksi) are measured directly below the notch roots, in good agreement withthe midline strain contour and stress computed by Chiesa7.

1300FI0.75 hr~

BD30.21 .ID04.09.E. H.mess.talc

...

.

“.... --- 600 MPa..”. —

NotchCenterline

0 I 1

.400 0 400 800 1200 1600

x, urn

E=l 95*75 GPa (28.3*2.2 ksi)

Figure 3. Nanoindentation results for flow stress beneath the score mark in a burst discannealed at 704°C (1300°F) / 0.75 hour. The trace is situated midway between the score rootand back surface of the disc.

Transmission electron microscopy of thin foils was attempted, in order to image thedislocation structures in burst discs. As anticipated, foil preparation to view the scoreligament was difficult, and no useful results were obtained.

In designing an emulation of the burst disc microstructure, we consider both flow stressand microstructure to be important. Magnetic moment, as a measure of transformationproduct, is an important aspect of that simulation. Schrinivas et a19have shown thatrolling of 316 is capable of producing martensite, the magnetic phase transformationproduct, although uniaxial tensile tests and other deformation processes do not typicallyinduce transformation. It is necessary to introduce plastic deformation in three-dimensional space including rotations, for martensite to form in 316. We experimentedwith other techniques, including channel die-extrusion, and scale-up of the indenter andspecimen size, and found only small (

representing specific parts of the ligament region shown in Figure 2. These specimensare discussed under Experimental Procedures.

The full-scale specimens were intended for several analyses, including accelerated agingstudies, and studies directed toward identifying thermally activated processes. Theaccelerated aging experiments would explore low temperature aging up to and includingexposure, in vacuum, to a temperature of 250”C. Activation volume measurements,based upon the methods of Feltham et allO, were planned in order to determine thecontrolling deformation mechanism(s) in the emulated microstructure. Specimens arestrained beyond yield to the flow stress regime and stress relaxation is then allowed tooccur as total strain and temperature are held constant. The relaxations are then analyzedaccording to the relationship

V* = - kT dh (t+tO)/ dz (1)

In which V* is the activation volume, k is Boltzmann’s constant, T is the temperature(K), z is the shear stress, t is the time of relaxation and tO,an integration constant, is

taken]o as one second. Often, tensile stress (o) is substituted in place of shear stress (T).

It is customary to obtain the area of the activated event through the relation V* = Ab inwhich b is the Burger’s vector and A is the area swept out by the activated event.Alternatively, V* = bzL in which the activated event is one Burger’s vector in width andL in length which may then be computed. It is now common to graphically present theresults in the form b3/V* vs. stressl 1. Stress relaxation studies are the tool of choice inthis study, since the available ductility, as will be seen, does not permit rate changeexperiments. The stress is taken as the instantaneous stress during relaxation and V* iscalculated from (1) using the slope at that stress during the relaxation. It is possible todiscriminate deformation mechanisms according to the stress intercept at b3/V* = O. Forexample, an intercept less than zero is associated with a frictional mechanism, anintercept of zero with dislocation intersection with dislocation multiplicationand an intercept greater than zero with the presence of athermal obstacles’ 1.

Experimental Procedures

and bypass,

A 15 cm diameter bar of 3 16L steel, hot finished, was sectioned first into plates 0.5, 1and 1.25 cm thick and 25 cm long. The final rolled thickness was 0.025 cm, givingthickness reductions of 50, 75 and 80%. This produced true strains of&= -0.7, -1.4, and -1.6. Room temperature, multi-pass rolling was performed in order to reduce the plates tofinal thickness. Quenching between passes minimized temperature increases. Thecomposition of that bar is shown in Table I. Specimens were then machined to finalshape by Electro-Discharge Machining.

‘“P.Feltham,G. Lehmann,R. Moisel,“StressRelaxationin Nickel”,Acts Metall.~, p. 1305,1969.1]N.R.Moody,S.L.Robinson,J.E. Angelo,iM.W.Perra,“ModelingtheEffectsof TemperatureonHydrogen-InducedCrackingin an AusteniticSuperalloy”,Proceedingsof the4th GreekNationalCongresson Mechanics,Vol 1,310 (1995).

12

Table 1. Compositionof the 316L bar stock in wt. %.

Cr i?i Mn Mo Si c N s P17.40 10.41 1.76 2.16 0.63 0.020 0.085 0.027 0.026

Metallographic sampling and hardness measurements confirmed that the microstructureof the hot-finished 15 cm diameter bar was uniform from center to edge. The carbon andnitrogen values are from LECO@ analyses.

Mechanical Testing and Accelerated AgingTesting was performed on a SATEC servomechanical test frame. Mechanically attachedextensometers were used to both measure and control specimen strain. The Satec testframe is configured with a digital data acquisition and control system that can beprogrammed to execute both the monotonic tensile tests and the strain controlledrelaxation tests that comprised this experimental program. In the latter case strain controlon the order of* 1 pstrain was achieved with the use of a high-resolution extensometer.

Aging effects on the room temperature mechanical properties of the cold-rolled stainlesssteel were measured through a series of monotonic uniaxial tensile tests. Test specimenswere flat “dogbone” tensile bars having 2.54 cm long gage sections that measured 0.635cm in width and 0.25 cm in thickness. AI] specimens were instrumented with an attached2.54 cm +50%, - 10% extensometer for strain measurement. The mechanical propertiestests were conducted at an initial strain rate of 0.02 see-l. Relaxation experiments wereconducted with specimens of the same geometry but with a 2.54 k 0.0635 cmextensometer for more precise strain control. Thermoplastic cooling was observed upontensile straining. Therefore, in order to meet isothermal test requirements, data taken inthe first few seconds after the crosshead was stopped were not used.

In addition to room temperature testing, a series of elevated temperature acceleratedaging tests were performed. The matrix of tests is shown in Table II. Following holdtimes (time 1 and time 2) at the indicated temperatures, specimens were cooled to roomtemperature and tested.

Table H. Accelerated aging studies test matrix.

Roiling Reduction Temperature, “C Time 1 Time 2

75% 150 14 days 28 days

75% 250 14 days 28 days

75% 7321 Hr/250 14 days 28 days

Results

Not all rolled materials were suitable for testing. The 50% cold-rolled material exhibitedlow strength (e 1030 MPa yield strength) and no significant martensite formation. The

80% cold-rolled material began to show edge cracking during rolling, raising concernsthat specimens would be vulnerable to defects. The 75% cold-rolled material was foundto be the most satisfactory material to test. The martensite concentration was slightlybelow that of the actual burst disc score zone, e.g. only about 4-5% martensite wasformed, compared to 6-10% in the score zone. [This result conflicts with the results ofShrinivas et a19who obtained more than 30% martensite concentration at similar strains.The difference is probably due to the much higher carbon concentration in 316 of0.08wt.’% compared to less than 0.03 in 3 16L.] Nevertheless, the desired yield strengthwas obtained.

Mechanical Testing and Thermal AgingThe principal objectives of these tests were twofold. The first was to assess the influenceof low temperature thermal aging on the as-rolled properties (specifically, strength andductility) of the alloy. The second objective was to determine if the martensite reversiontreatment reduced the susceptibility of the alloy to any thermal aging-induced changes inmechanical properties.

Since we expected to observe only subtle changes in the measured properties of the alloyit was important to determine the general reproducibility of the data. To that end, thestress-strain behavior for four specimens was determined in the as-rolled condition asshown in Figure 4. The three replicate tests reveal the good uniformity in cold workimparted to the alloy during rolling. Subtle yield drops are suggested by the data,although they are not visible at the resolution of the figure.

The results for 4 specimens tested in the 75% cold-rolled condition are summarized inTable III. Yield and ultimate strengths are reproducible to better than 1%. Strainmeasurements are also quite reproducible.

Table Ill. Tensile properties of replicate as-rolled specimen cold rolled to 75thickness reduction Yo.

Sample # Yield UTS Unif.Strain Frac. Strain(MPa) (MPa) (%) (%)

,1 1197 1302 ~.16 12.34~ 1181 1303 2.13 12.51

1181 1291 2.28 12.621: 1188 1301 2.23 12.34

/ Avg. 1187 1299 2.20 12.43 1Std. Dev. ~7.6 &5.5 &o.07 *().14

Aging the alloy at 250”C for 14 and 28 days after cold-rolling to 75% has a significanteffect on both strength and ductility, as shown in Figure 5. The UTS of the alloyincreased by approximately 109i0 (1299 MPa to about 1462 MPa after 14 days attemperature) while uniform strain (strain to UTS, the onset of plastic instability) andoverall ductility decreased. After 14 days at 250”C, uniform strain fell by near] y 25 ~0from 2.2% to 1.5% while strain to failure decreased from about 12.4% to about 8.5%.

14

150C I 1 r

316L Stainless Steel75”/. Reduction in Thickness

oI I

o 5 10 15

Strain (%)

Figure 4. Tensile behavior of rolled stainless steel specimens.

1500

0

Effect of Post-Rolling Anneal

— As-rolled— 14 days @ 250C—28 days I@ 250C

I t L

o 5 10 15Strain (Y.)

Figure 5. Effect of 250°C thermal age on the stress-strain curves for 75% cold-rolledstainless steel.

15

.. --*..

. . . .

Only a small additional effect on mechanical properties was observed after 28 days at250”C, suggesting a saturation of the thermal aging effect.

Room temperature aging of burst discs is more rapid than that observed in experimentallysimulated midline material (at &= -1.4, identified in Figure 2 directly below the root ofthe score). Actual burst discs experience approximately 60% of their total burst strengthincrease in 60 days at room temperature, while the rolled midline-equivalent materialexperiences about a 10% (17.2 MPa) increase at room temperature. The reasons for thisslow aging effect are discussed later.

As noted previously, the rolled specimens are intended to simulate the behavior of thescore ligament, both in the as-rolled condition and following the aging schedule. Thepercentage strength increase observed in the rolled specimens is lower and develops moreslowly than in the burst discs, but is consistent with the burst pressure increase observedafter extended aging. Thus it is taken to simulate that behavior.

As the strength increase asymptotically approaching a limiting value, shown in Figure 6,the fracture strain approaches an asymptotic lower bound, as shown in Figure 7.Following aging at 150”C, strength and ductility of the worked alloy were affected to alesser degree than at 250°C. Figure 8 shows the stress-strain behavior of the 75% cold-worked alloy after aging 15 days at both 150”C and 250”C. These curves are compared toa representative as-rolled curve. These tests reveal that the as-rolled stainless steel isthermally unstable at temperatures as low as 0.25 T~P. This result implies that the time-dependent burst pressure increase is derived from the same phenomena observed in therolled specimens. Furthermore, at elevated temperature, short times are required toproduce significant changes in properties; near room temperature, the time necessary forobservable changes is greater, indicating that the mechanism is thermally activated.

The last series of tests were undertaken to test whether the thermal instability was alsopresent in rolled specimens that had been subjected to the martensite reversion-anneal(732°C/1 hr). Figure 9 shows the tensile behavior of the 316L cold-rolled material afterthe 732°C reversion-anneal (duplicate specimens). The properties of the alloy are quitereproducible. As expected, the heat treatment results in a decrease in strength and anincrease in ductility compared to the as-rolled specimens.

The effect of the 250°C/15 day aging treatment on the properties of a reversion-annealedspecimen is shown in Figure 10. Unlike the as-rolled specimens, the aging treatment hasno appreciable effect on ductility and strength; the strength may be even slightly reduced.The thermal instability exhibited by the as-rolled material is eliminated by the reversion-anneal. As such the alloy no longer is susceptible to the time or temperature inducedchanges in mechanical properties, within the boundaries of time and temperatureexamined.

A sample room temperature stress relaxation curve is shown in Figure 11. Note thatmaintaining stable temperature is difficult due to thermoplastic cooling; accordingly, datawas only used when temperature was constant within 0.5”C. Activation volume

16

1500 I I [ I I-B

● Yld■ UTS

1400 -1●

1?

L

● ●

g

: g

●

~ 1300mg

z1200

Change in Strength -After Aging @ 250C -

1100r. I I I 1 I 1

0 5 10 15 20 25 30

Days at Temperature

Figure 6. Evolution in strength with aging time at 250”C.

2.2 ~ 5 I I I I IChange in Uniform StrainAfter Aging @ 250C

2 ~

q 1.9 :0

m

1.6 ;

1.5 : ●●

1.4 “’ I I● 1 I I

o 5 10 15 20 25 30

Days at Temperature

Figure 7. Strain to onset of plastic instability increases with increasing aging time.

17

.. ... ,- .,.=...—-. --Y. .......-----,. ..=..,,*.,..-..-. --- . -.—--em-,-,, -,.,

1500

1250

1000

750

500

250

0,,,,,,m:

I

o 5 10 15Strain (Y.)

Figure 8. Influence of aging temperature on mechanical properties of 75% cold-worked stainlesssteel.

1500 i I 1Reversion Anneal

1000-

500 -

Io~o 5 10 15 20

Strain ( ?’O)

Figure 9. Tensile properties of reversion annealed cold worked stainless steel.

18

1500 1 I 1

; 1000-az

mIna$ 500-. — Aged @ 250C

— As annealed

rAging Effect on -

Reversion Anneal Properties -0 1 ! 10 5 10 15 20

Strain ( % )

Figure 10. Tensile properties of reversion annealed stainless steel are unaffected by thermalaging.

1300

1200

1100

CWSS-7-75(RELAX)8d 2:4221 Phl 9/24/98

I a , , , t i o

# , , ! I , ,2102 7102 1.210’ 4.710’2.210’2.7 10’3.21033.710’

24.5

24

23.5

:

323 ~

~c3

22.5~

22

21.s

21

Time ( s )

Figure 11. A sample stress relaxation curve for 75% cold rolled stainless steel.

.... - -

measurements are shown in Figure 12A for 50 and 75% cold rolled 316L, and forreversion-annealed 75’%0rolled material. The 75% cold rolled state exhibits no significantdifference in slope (b3/V* vs stress), or stress axis intercept of bq/V* at b3/V* =0, whentested after one week of aging. The offset in the stress axis intercept between as-formedand reversion-annealed material may be due to the elimination of the martensite. Pre-and post-anneal specimens appear to behave similarly to IFJ903 (Figure 12B), that is, anintercept greater than zero is obtained at bs/V*=O.

Discussion

Assuming that we have adequately emulated the microstructural state of the midline ofthe ligament, these results lead to the practical conclusion that the burst disc will notexhibit further aging after experiencing the reversion-anneal. Limitations to themicrostructural emulation include 1) a slightly lower volume fraction of martensite in therolled product, 2) a reduced rate of room temperature aging compared to the burst discand 3) differences in the strain rates and total strain between forming the burst discligamerlt and the rate of deformation imposed during cold-rolling of the tensile

specimens. In order to understand the roles played by these factors, it is important toclarify the mechanisms controlling deformation and aging rate. In the following we

discuss the deformation mechanisms.

Most authors cited3”Ghave demonstrated or assumed that carbon is crucial to the agingprocess. We have shown, on the basis of yield drops and reaction kinetics that the effectsobserved in this study are consistent with the diffusion of carbon to dislocations, thereeither to precipitate or to form atmospheres in the dislocation strain fleid. Our hypothesisconcerning the source of the aging effects is therefore straightforward, and builds uponprevious studies of strain aging in stainless steels. First we summarize the observationsand the phenomena that a model must describe. We observe that extreme states ofdeformation are required to observe aging in low carbon stainless steels, in agreementwith previous investigators3-b. The deformation sensitivity is such that a high strainmicrostructure (&=1.4) appears to age while a microstructure formed at lower strain(&=O.7) seems not to age at all. Aging appears to be thermally activated, and occurs atappreciable rates at or near room temperature, thus requiring a low activation enthalpy inany model proposed. Furthermore, the extent of the yield strength increase appears tosaturate, and low temperature (732°C) annealing not only halts this increase but revertsthe yield strength to approximately it’s original value. Finally, the activation volumebehavior appears to be athermal in nature, arising from an intensely cold workedstructure, rather than from a precipitation strengthened microstructure.

Analysis of the Activation EnergySince the strength increase is thermally activated, measurement of the temperaturesensitivity of the event is needed to identify the controlling mechanisms. Fitting anArrhenius rate equation to the ultimate tensile strength data of Figure 8 shows that AH =18 kJ/mole (4.3 kcal/mole) for the 75% cold rolled 3 16L with a goodness of fit (Rz) of0.995. Ulitchney and Gibalas cite AH~~for interstitial carbon self diffusion in austenitic

20

1.4

12

10

$0’8<n

0.6

0.4

01

0.(

m7wfkMldColdRO!ted316L \

91Es&mMiQlll%b&?ti A Z.nhmd<

p-6J6nc(133m:

: mud

(:

c

0,,1

A

204 400 coo 800 lCMStress,MPa

—1X4

0.020 I

0,015-

:@y0.010-Q

0!005-

l-l“o 5oil 1000 1500 2000

Stress,MPa

Figure 12. A Reciprocal activation volume normalized to b3 as a function of flow stress for as-ro~ed and reversion annealed 316L stainless steel. B. Activation volumes for other alloys areshown for comparison [from Moody et al”] at small values of b3/V.

steels as 141.4 kJ/mole (34*5 kcal/mole), indicating that interstitial carbon diffusion isnot the rate controlling event for aging. The low value of AH explains how the agingphenomenon can occur at room temperature; however it fits no known single diffusingspecies. The lower AH for aging vs. self-diffusion may be due to vacancy completing, asdiscussed by a number of authors3”G. A detailed analysis of the temperature sensitivitiesof interstitial carbon self-diffusion and carbon vacancy complex diffusion in the presenceof excess (non-thermal) vacancies, arising from intense cold work, may be found in theappendix.

Analysis of the Kinetics of the Rate of Strength IncreaseAn analysis of aging kinetics based upon the kinetics of diffusion controlled growthallows a measure of the degree of acceleration obtained by the elevated temperatureaging. Furthermore, it demonstrates why aging rates differ exponentially betweenmicrostructure, such that some age rapidly while others appear stable. We assume thatcarbon is diffusing to dislocations, and that the dislocations are spaced uniformly. Theform of the deformation obstacle which carbon takes upon arrival at a dislocation neednot be specified in this analysis, since diffusion is rate controlling. The theory of thekinetics of diffusion controlled growth describes kinetic phenomena in the form

21

.. .. . ;T.v.= ~— ..\ ... ~ ,-,,. -:-, ,,$ -----,-.m.v— .?,....,. . Z,. .- --- $.

X = l-exp-(t/T)m (2)

where X is the extent of completion of the reaction with bounds of O and 1, t is the time,

T is a characteristic time at which 0.63 (l-e-i) of the reaction is complete, and m describes

the order of the mechanism. For example, this expression is also useful in describing thegrowth of second phases. For X the degree of completion of the reaction, we use in thiscase the fraction of the total strength increment developed at time t. Using the 250”C data(the ultimate tensile strength) of Figure 6, and plotting in in (l/( l-x)) against in t gives m= 1.02. Although only three data points are available, the goodness of fit is 0.999.

Ham’z showed that m= 1 describes the long-term collection of atoms by dislocations,when tetragonality of defects is considered. An exponent of 1 is also appropriate to thegrowth of needle-shaped precipitates 3. These results are consistent with the previousthermal activation data, indicating that the strength increase is controlled by the diffusionof carbon atoms to dislocations. The result is consistent with carbon precipitation ondislocations ‘z. Thus the hypothesis of carbon transport to dislocations is supported bythe agreement between theoretical and observed kinetics of the rate of strength increase.The burst disc data of Meyerz could not be analyzed in this framework due to theheterogeneous nature of burst disc microstructure.

Further discussion of the mechanisms mentioned above may be found in the appendices.

Limitations of the StudyA limitation in this study is that the multipass-rolled microstructure may differ infundamental ways from the scored disc microstructure. The disc score is formed rapidlyat room temperature, in about one second, followed by a hold for 10-15 seconds. Therolling process required about 30 minutes of multipass rolling, with repeated water bathsto minimize temperature rise to the 40-50”C range. Aging and recovery are likely to haveoccurred in that 30-minute interval. Thus the zero time measurements in the emulatedmicrostructure may already include some pre-aging (at slightly elevated temperature),and the kinetic phenomena may be altered. Pre-aging would be expected to reduce theroom temperature response, to have some effect on the accelerated aging response, andpotentially to alter the activation enthalpy. Differences in aging rates attributable todislocation structures formed at high rates versus low rates are discussed in Appendix D.

‘z F. S. Ham, “Stress-AssistedPrecipitationon Dislocations”, Journalof Applied Physics 3Q, 915-926(1959), and “Diffusion-Limited Growth of PrecipitateParticles”, Journalof Applied Physics,Q1518(1959).13M.E.Fine Phase Transformationin Condensed Solids, McMillan, New York New York, 1964.‘JL.E. Murr and F.I. Grace, Residual Structureand Mechanical Properties of Alpha Brass and StainlessSteel Following Deformation by Cold Rolling andExplosive Shock Loading, Trans. AIME, 2225, vol 245,1969.15C. Donadille, R. Vane, P. Dervin and R. Penelle, “Development of Texture and Microstructure DuringCold-Rolling and Annealing of F.C.C. Alloys: Example of an Austenitic Stainless Steel, Acts Metall. ~,1547-1571, 1989.

22

No attempt has been made to compensate for these potential specimen preparationeffects.

Conclusions

1. The stability of the tensile properties, and by extension the burst pressure of postreversion-anneal burst discs, have been demonstrated through microstructural emulation,accelerated aging, and modeling of both the microstructural sensitivity and temperaturedependence of aging. We emulated two of the most important microstructural features ofthe burst disc ligament, that is, martensite production and flow stress (dislocationstructure) characteristic of the midline of the ligament. Some differences still existbetween the behavior of the simulated material and burst discs. While the emulatedmaterial ages, it does so more slowly than actual burst discs. This may indicate that themidline-simulating structure does not represent the burst pressure-controllingmicrostructure in the burst disc. It may also indicate that the preparation methodscompromised the aging kinetics and magnitude of the effect. A desirable step to achievefull confidence in these conclusions is to reproduce these results using reversion-annealedburst discs.

2. The measured activation enthalpy of 18 kJ/mole (4.3 kcal/mole) for ultimate tensilestrength increase is inconsistent with diffusion of carbon. An alternative mechanism, the(substitutional) diffusion of C-V complexes was investigated. The diffusion activationenthalpy of C-V complexes was modeled as Q,ff = EMv - Ebc-v (in the presence of nOn-thermal excess vacancies), predicting a carbon-vacancy binding energy of the order of 83kJ/mole, which is at the upper bounds of reported values [summarized in reference 6].The reaction kinetics are consistent with transport of a species such as carbon todislocation lines, presumably pinning the dislocations and enhancing tensile strength.Applying a mathematical solution to the long-term diffusion problem of defects todislocations due to Ham12 has allowed a microstructurally consistent understanding of thediffering effects that cold work has on the rate of aging of unstable microstructure. Themodel is consistent with the behavior of burst discs; however, it is unable to account forthe effects of a highly inhomogeneous dislocation density in which aging kinetics may becontrolled by high local densities rather than average dislocation densities.

3. The activation volume measurements demonstrate behavior which resembles that ofprecipitation-strengthened materials such as IN903, in which athermal obstacles controldislocation flow. The measurements also demonstrate the high stability of the workedmicrostructure against aging and thermal annealing. Furthermore, the activation volumemeasurements establish that the martensitic phase per se does not control the plastic flowof the worked metal. The reversion-annealing behavior is consistent with knownmicrostructural effects at high cold-rolled strains in 3 16L, in which persistent dislocationstructures that are resistant to annealing are observed. The activated event L is computedto be less than or equal to lb, suggesting dislocation intersection and bypass as thedeformation controlling event, an apparent contradiction of the athermal behavior noted.

4. This analysis leads to the conclusion that prevention of the undesired agingphenomenon, without resort to partial annealing, requires avoiding the extreme

deformation states that give rise to the aging phenomenon.

Acknowledgements

We would like to acknowledge many helpful discussions with Professor Ron Gibala ofthe University of Michigan, and with Darcy Hughes and Brian Somerday of SNL. Inaddition, Andrew Gardea performed the metallography while Mike Tootle performed themechanical testing. Nancy Yang contributed her expertise in thin film electronmicroscopy.

. ... . .

Appendices

A. Hypothesis for the Mechanism Controlling Time Dependent Strengthening

In order to explain the aging phenomenon we hypothesize a time dependent strengtheningmechanism which depends upon carbon redistribution to dislocations wherein pinningpoints are formed. We assume that once carbon arrives at the dislocations, formation ofobstacles is rapid. The rate of carbon redistribution is assumed to be greatly acceleratedby the presence of excess vacancies produced by cold work, and the model exhibitsstrong dependence upon sink spacing (mean free path) which is related to the degree ofcold work. The observed temperature sensitivity (low activation enthalpy) requires theformation of a large excess of vacancies from cold work (above the thermal equilibriumconcentration), and the association of carbon with these vacancies into C-V pairsexhibiting a low migration energy. During the 732°C reversion anneal, excess vacanciesare assumed to be annihilated while carbon is moved into solution, removing thestrengthening effect of precipitated carbon on dislocations. Self interstitial formed bycold work are assumed immobile to higher temperatures, in agreement with otherinvestigators3-6.

B. Analysis of the Activation Energy Utilizing Vacancy-assisted AcceleratedDiffusion

This work draws upon that of Ulitchney and Gibala6. An explanation for the lowtemperature sensitivity of the aging process may be derived from an understanding ofvacancy partitioning, when both free vacancies and carbon-vacancy (C-V) complexesexist. Assuming that C-V pairs are mobile, and are in dynamic equilibrium withinterstitial carbon and free vacancies then the total vacancy concentration may be writtenas CvT= Cv F + Cc-v, in which Cv F is the free vacancy concentration, and Cc-v is theconcentration of C-V pairs. Following the derivation of Ulitchney and Gibala6 theeffective diffusion coefficient of vacancies can then be written

D=CO%Z,CCExp(Ebc-v/kT)Exp-(EFv+E~v)/kT (3)

In which CO is the initial vacancy concentration, v is a vibrational frequency, 21 is a

crystallographic coordination number, Cc is the initial carbon concentration, E~c-vis thebinding energy of carbon atoms to monovacancies, and E~ v and EMv are the formationand migration energies for monovacancies in the metal, respectively. COmay be replacedby Cv T to describe a variable diffusivity during the aging, as excess vacancies areconsumed.

The effective temperature dependence of the carbon-vacancy diffusion in (2) is then

QEFF = EF ‘+ EMv - E,c-v (4)

which states that the effective activation enthalpy is equal to the vacancy self diffusionenergy minus the binding energy of carbon to vacancies. When the number of vacancies

25

greatly exceeds the thermal contribution, as hypothesized to result from extreme levels ofcold work, we may ignore EF ‘. During the aging transient we then obtain Q~FF= EMv -E~c-v. From literature values, EMv - 0.4QS~ - 100 kJ/mole (24 kcal/mol) in stainless

steel. Using Q~~F- 18 kJ/mole (4.3 kcal/mole), the binding energy E~c-v is approximately82-83 kJ/mole (-20 kcal/mole). This value is at the upper bound of reported valuesb,indicating rough agreement with experiment. Following the end of aging when thevacancy excess has been consumed, thermal equilibrium would again control the vacancypopulation, the number of vacancies would become small, and the diffusion rate wouldbecome slow. At that time, the effective activation enthalpy Q~~~would become largerby the value of E~ v . As a result, QEmc-vexceeds Q~~(c),and interstitial c~bon diffusionwould control the rate of transport of carbon diffusion to dislocations.

The effect of the reversion anneal is to consume excess vacancies, thus slowing the rapidtransport of carbon. Thus the above diffusion argument explains why the strengthincrease stops following the reversion anneal. In addition, the anneal removes carbonalready transported to dislocations, putting it back into solution, thereby removing thestrength increase caused by aging.

C. Quantification of Thermal Acceleration of Aging

At the beginning of the discussion, we hypothesized that the effect of the reversionanneal was to consume excess vacancies. From the preceding discussion, we see that wecan define the degree of acceleration of the aging at 250”C using the characteristic time T,

and the acceleration factor z 25/ ~ 250.Using m =1, the data of figure 8, and lc of 7.6 MPa(see Table III), we obtain ~‘5 = 741 &40 days and t ’50= 7-1 A 0-7 days, from which weobtain z‘5 / ‘C250= 106 & 16, which is the degree of acceleration of aging at 250”Ccompared to 25°C. Previously we asserted that annealing resulted in cessation of aging;we may now quantify that statement. We annealed 28 days at 250”C, and saw no strengthincrease (X-O). From the relationship t25/~z5= t250/&50,28 days at 250°C is equivalent to

2968&448 days at 25”C. Thus no aging effect should be observed for that period of time(8.1A 1.2 years).

D. Kinetics of Aging in Different Microstructure

Of particular interest is why heavily cold-worked microstructure such as found in theburst disc ligament age at high rates at room temperature, while our 75% cold-rolledspecimens age more slowly, and the 50% rolled specimens appear to not age at all. Usingthe model provided by Hamlz we compare the aging rates of different microstructurearising from a variety of levels of cold work. In this model, we use the dislocationdensity at different levels of cold work as a parameter. We assume that a defect such asC-V complexes arising from excessive cold work must ‘sink’ to the dislocation structure.Once there, (unidentified) pinning points are formed, increasing the flow strength of themicrostructure. Solution of the long-term diffusion problem for both edge and screwdislocations, and for both regular and random arrays provides a relationship between thesink radius r,, and the characteristic time (z) of the diffusion problem. Ham assumed acylindrical array of dislocations in which the sink radius (r.) is related to dislocation

26

. ....... ,=,—.-y ----7 . . ..-. -. . .. . . ,, .Tcm.—m - , “.....~~ —. -~— -- .,, -,

density by r, = (~~) ‘1’2in which p is the dislocation density in length per unit volume. He

then related the parameter D~zp, where D is the diffusion coefficient of the species in

question, to the variable (l/R(p)* n), in which R is the capture radius of the sink.

Using Ham’s relationship we may now illustrate both aging trends and the sensitivity of ~

to dislocation density (P) . We use the dislocation density data of Murr and GracelJ for

brass, since data for 3 16L over a wide range of cold work are unavailable. A change indislocation density from that of a 5-10% cold worked material (lOIZ – 1013 m-z) to thehighly worked level typical of the burst disc material (greater than 1015m-z) reduces thecharacteristic time by about a factor of 400. Thus to reach a fraction reacted X (1-l/e)which requires 60 days in a burst disc will require decades in material cold worked tomoderate strains, and the material would be seen as not aging. (This assumes that thenecessary vacancy excess, postulated here and elsewhere, continues to exist. At smallstrains and low deformation rates, this will not be true, further diminishing the magnitudeof the effect.) Consistent with the example, even our 50% reduced 3 16L exhibited nomeasurable aging within the bounds of the experiment.

Similarly, the difference in rate of aging between our 75% cold-rolled material and theburst disc behavior may be examined using equation (2). Recall from Figure 2 that veryhigh strains, to &>2, are predicted in the ligament. Based upon Murr’s dislocationdensities 14, and Ham’slz first eigenfunction solution, the characteristic time shoulddecrease by a minimum factor of 2.5. This trend is correct in direction, that is, the agingrate increases with greater cold work, however it underpredicts the relative aging rates.The differences may arise from the extreme inhomogeneity of the dislocation densitywithin the microstructure, as was shown by Donadille et al]5, compared to the uniformstructures assumed within the model. We know also that differences exist betweenmicrostructure formed at high rates vs. those formed at low rates. The rolledmicrostructure would tend to have more well-defined dislocation walls and fewer freedislocations between cell walls than would high-rate-formed microstructure (burst discscores). Thuis the high rate microstructure might have a greater volume of material toage, providing a greater overall rate and extent of strengthening. A much more detaileddescription of dislocation structures and an understanding of the obstacles formed bycarbon precipitation are required to refine this analysis, and we must be satisfied withillustrating trends.

E. Activation Volume

Specimens were not aged sufficiently to allow activation volume measurements to detectthe potential effects of carbon precipitation on V*. The following observations applyonly to unaged or short-term aged cold worked material.

The results in Figure 12A indicate that the activation volume behavior is stronglyathermal, and exhibits a high degree of microstructural stability against thermalperturbations. The observations of Donadille et a115, who observed inhomogenousrecovery and recrystallization in heavily worked 3 16L, are consistent with the aboveobservations of microstructural stability. Donadille observed microbands15 at strains

2’7

.—

exceeding 70910,as well as rhombohedral shaped structures, which were very resistant torecovery and recrystallization, and which would not have recovered at the temperature ofthe reversion-anneal i5. These apparently highly integrated dislocation structures may bethe source of the athermal behavior. Much more detailed descriptions of these structuresare required to clarify the occurrence of dislocation intersections as deformation-controlling events in the presence of these structures.

The length of the microstructurally controlling activated event L may be computed fromV*=b2L. Since b3/V* is typically about one at the beginning of stress relaxation, L is ofthe order of one burgers’ vector or smaller. This observation suggests that flow iscontrolled by dislocation intersection and bypass, which presents a difficulty ininterpretation. A value of L less than lb appears to require cooperative motion ofdislocations in which a bypass event is partially compensated by a back-relaxation ofother dislocations in the tightly woven dislocation structures. This issue cannot beresolved with the current information.

28

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